What makes a writing system such, and why emoji are not a writing system?
By using those two websites, you can easily find the definition of a writing system, which is "[...] a method of visually representing verbal communication" and reflect on the fact that since emoji aren't used to encode an oral message, they don't form a writing system.
Emoji certainly classify as related to a "linguistic system" even if you don't think they have a direct verbal counterpart. Non-verbal languages certainly exist and many of them have forms of writing systems and some of those are encoded in Unicode, too. Emoji isn't the only "writing system for a non-verbal language system" encoded in Unicode.